An instanton take on some knot detection results

John A. Baldwin; Steven Sivek

doi:10.1090/pspum/109/01991

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arXiv · 2211.03743

An instanton take on some knot detection results

John A. Baldwin·Steven Sivek

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Abstract

We give new proofs that Khovanov homology detects the figure eight knot and the cinquefoils, and that HOMFLY homology detects $5_2$ and each of the $P(-3,3,2n+1)$ pretzel knots. For all but the figure eight these mostly follow the same lines as in previous work. The key difference is that in honor of Tom Mrowka's 60th birthday, the arguments here use instanton Floer homology rather than knot Floer homology.

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John A. Baldwin, Steven Sivek. 2022-11-07. An instanton take on some knot detection results. https://doi.org/10.1090/pspum%2F109%2F01991

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